Question 757481
Number_______________Number_Squared
2____________________4
3____________________9


Look at this in the other direction.  {{{sqrt(4)}}} is 2.
{{{sqrt(9)}}} is 3.  Can you find any squares between 4 and 9?  No.  Can you find some numbers between 4 and 9?  Yes.


Pick any number between 4 and 9 EXCLUDING 4 and 9.  Would the square root be rational or irrational?  Would this square root be within the limits of between 2 and 3 or not?  

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And if that did not give you clear enough impression for finding irrational numbers between 2 and 3, let us see an expansion of the above table:


Number_______________Number_Squared
2____________________4
?____________________4.3
?____________________4.77
?____________________5
?____________________6
?____________________6.51
?____________________6.94
?____________________7
?____________________8
3____________________9